Abstract
This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin–Bona–Mahony–Peregrine–Burgers (BBMPB) equation. The various types of wave structures are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave, and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately find solutions and predict the behaviour of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behaviour of the solutions, some 3D plots and their respective contour level are shown, choosing different values of the parameters.
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